Higher November 2023 Paper 6 Q12

OCRHigherCurrent spec4 marksBasic Probability Sets

12 A cafe owner recorded information about customer orders for coffee.
They recorded whether the customer asked for milk (M) and whether the customer asked for sugar (S).

The results are shown in this Venn diagram.

Venn diagram with overlapping circles M and S in a universal set: 25 in M only, 11 in both M and S, 18 in S only, and 16 outside both circles

(a) One of the customers is chosen at random.

Find the probability that the customer asked for sugar. [2]

(b) One of the customers is chosen at random.

Find the probability that the customer asked for sugar given that they asked for milk. [2]

Answer	Marks	Part marks and guidance
\(\frac{29}{70}\) oe	2	B1 for 11 + 18 or 29 or for \(\frac{n}{25 + 11 + 18 + 16}\) or \(\frac{n}{70}\) with \(n < 70\)	Accept 0.41[4…] or 41[.4…]%

Mark scheme (b)

Answer	Marks	Part marks and guidance
\(\frac{11}{36}\) oe	2	B1 for \(\frac{11}{n}\) with \(n > 11\) or for \(\frac{n}{25 + 11}\) or \(\frac{n}{36}\) with \(n < 36\)	Accept 0.30[5..] to 0.31 or as %